/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <https://www.quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT

 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS

 FOR A PARTICULAR PURPOSE.  See the license for more details.

*/

/*! \file dplusdminus.hpp

    \brief \f$ D_{+}D_{-} \f$ matricial representation

*/

#ifndef quantlib_d_plus_d_minus_h

#define quantlib_d_plus_d_minus_h

#include <ql/methods/finitedifferences/tridiagonaloperator.hpp>

namespace QuantLib {

    //! \f$ D_{+}D_{-} \f$ matricial representation

    /*! The differential operator \f$  D_{+}D_{-} \f$ discretizes the

        second derivative with the second-order formula

        \f[ \frac{\partial^2 u_{i}}{\partial x^2} \approx

            \frac{u_{i+1}-2u_{i}+u_{i-1}}{h^2} = D_{+}D_{-} u_{i}

        \f]

        \ingroup findiff

        \test the correctness of the returned values is tested by

              checking them against numerical calculations.

    */

    class DPlusDMinus : public TridiagonalOperator {

      public:

        DPlusDMinus(Size gridPoints, Real h);

    };

    // inline definitions

    inline DPlusDMinus::DPlusDMinus(Size gridPoints, Real h)

    : TridiagonalOperator(gridPoints) {

        setFirstRow(0.0,0.0);                   // linear extrapolation

        setMidRows(1/(h*h),-2/(h*h),1/(h*h));

        setLastRow(0.0,0.0);                    // linear extrapolation

    }

}

#endif